2,772 research outputs found

### Vector bundles on the projective line and finite domination of chain complexes

Finitely dominated chain complexes over a Laurent polynomial ring in one
indeterminate are characterised by vanishing of their Novikov homology. We
present an algebro-geometric approach to this result, based on extension of
chain complexes to sheaves on the projective line. We also discuss the
K-theoretical obstruction to extension.Comment: v1: 11 page

### Paradigms for Parameterized Enumeration

The aim of the paper is to examine the computational complexity and
algorithmics of enumeration, the task to output all solutions of a given
problem, from the point of view of parameterized complexity. First we define
formally different notions of efficient enumeration in the context of
parameterized complexity. Second we show how different algorithmic paradigms
can be used in order to get parameter-efficient enumeration algorithms in a
number of examples. These paradigms use well-known principles from the design
of parameterized decision as well as enumeration techniques, like for instance
kernelization and self-reducibility. The concept of kernelization, in
particular, leads to a characterization of fixed-parameter tractable
enumeration problems.Comment: Accepted for MFCS 2013; long version of the pape

### Fast algorithms for min independent dominating set

We first devise a branching algorithm that computes a minimum independent
dominating set on any graph with running time O*(2^0.424n) and polynomial
space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A
branch-and-reduce algorithm for finding a minimum independent dominating set in
graphs, Proc. WG'06). We then show that, for every r>3, it is possible to
compute an r-((r-1)/r)log_2(r)-approximate solution for min independent
dominating set within time O*(2^(nlog_2(r)/r))

### Direct and indirect orthotic management of medial compartment osteoarthritis of the knee

Osteoarthritis (OA) is a painful condition and affects approximately 80% of individuals by the age of 55 [1], with knee OA occurring two times more frequently than OA of the hand or hip [2].The condition is more prevalent in the medial compartment and restricts the daily lives of individuals due to pain and a lack of functional independence. Patients with medial compartment osteoarthritis often have a varus alignment, with the mechanical axis and load bearing passing through this compartment with a greater adduction moment leading to greater pain and progression of osteoarthritis [3]. Surgery for the condition is possible although in some cases, particularly younger patients or those not yet requiring surgery, clinical management remains a challenge. Before surgery is considered, however, conservative management is advocated, though no one treatment has been shown to be most effective, and there are few quality biomechanical or clinical studies. Of the conservative approaches the principal orthotic treatments are valgus knee braces and laterally wedged foot inlays. Studies of knee valgus bracing have consistently demonstrated an associated decreased pain and improved function [4], and greater confidence [5]. A laterally wedged foot inlay has a thicker lateral border and applies a valgus moment to the heel. It is theorised that by changing the position of the ankle and subtalar joints during weight-bearing [6] the lateral wedges may apply a valgus moment across the knee as well as the rearfoot, with the assumed reduction on load in the medial knee compartment [7]. However, there has been no study to directly compare these orthotic treatments in the same study. The aim of this research is to investigate the efficacy of valgus knee braces and laterally wedged foot inlays in reducing the varus knee moment

### Connecting Terminals and 2-Disjoint Connected Subgraphs

Given a graph $G=(V,E)$ and a set of terminal vertices $T$ we say that a
superset $S$ of $T$ is $T$-connecting if $S$ induces a connected graph, and $S$
is minimal if no strict subset of $S$ is $T$-connecting. In this paper we prove
that there are at most ${|V \setminus T| \choose |T|-2} \cdot 3^{\frac{|V
\setminus T|}{3}}$ minimal $T$-connecting sets when $|T| \leq n/3$ and that
these can be enumerated within a polynomial factor of this bound. This
generalizes the algorithm for enumerating all induced paths between a pair of
vertices, corresponding to the case $|T|=2$. We apply our enumeration algorithm
to solve the {\sc 2-Disjoint Connected Subgraphs} problem in time
$O^*(1.7804^n)$, improving on the recent $O^*(1.933^n)$ algorithm of Cygan et
al. 2012 LATIN paper.Comment: 13 pages, 1 figur

### Distributed Approximation of Minimum Routing Cost Trees

We study the NP-hard problem of approximating a Minimum Routing Cost Spanning
Tree in the message passing model with limited bandwidth (CONGEST model). In
this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes
that minimizes the sum of distances between all pairs of nodes. In the
considered model every node can transmit a different (but short) message to
each of its neighbors in each synchronous round. We provide a randomized
$(2+\epsilon)$-approximation with runtime $O(D+\frac{\log n}{\epsilon})$ for
unweighted graphs. Here, $D$ is the diameter of $G$. This improves over both,
the (expected) approximation factor $O(\log n)$ and the runtime $O(D\log^2 n)$
of the best previously known algorithm.
Due to stating our results in a very general way, we also derive an (optimal)
runtime of $O(D)$ when considering $O(\log n)$-approximations as done by the
best previously known algorithm. In addition we derive a deterministic
$2$-approximation

### The Densest Hemisphere Problem

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-72-C-0259National Science Foundation / MC76-1732

### Approximation Algorithms for the Capacitated Domination Problem

We consider the {\em Capacitated Domination} problem, which models a
service-requirement assignment scenario and is also a generalization of the
well-known {\em Dominating Set} problem. In this problem, given a graph with
three parameters defined on each vertex, namely cost, capacity, and demand, we
want to find an assignment of demands to vertices of least cost such that the
demand of each vertex is satisfied subject to the capacity constraint of each
vertex providing the service. In terms of polynomial time approximations, we
present logarithmic approximation algorithms with respect to different demand
assignment models for this problem on general graphs, which also establishes
the corresponding approximation results to the well-known approximations of the
traditional {\em Dominating Set} problem. Together with our previous work, this
closes the problem of generally approximating the optimal solution. On the
other hand, from the perspective of parameterization, we prove that this
problem is {\it W[1]}-hard when parameterized by a structure of the graph
called treewidth. Based on this hardness result, we present exact
fixed-parameter tractable algorithms when parameterized by treewidth and
maximum capacity of the vertices. This algorithm is further extended to obtain
pseudo-polynomial time approximation schemes for planar graphs

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